1. Technical Field
The present invention relates to apparatus and methods for fluid flow measurement in general, and to apparatus and methods for fluid flow measurement operable to determine a Reynolds number for the fluid flow in particular.
2. Background Information
SONAR type fluid flow meters operable to measure flow parameters traveling through a pipe can be calibrated as a function of the Reynolds number of the fluid flow. The Reynolds number (Re) may be described as a dimensionless number that gives a measure of the ratio of inertial forces (ρL2V2) to viscous forces (μLV). The Reynolds number of a fluid flow may be mathematically represented as follows:
                    Re        =                              ρ            ⁢                                                  ⁢            VL                    μ                                    (                  Eqn          .                                          ⁢          1                )            where “ρ” is the fluid density, “V” is the velocity of the fluid, “L” is the length scale, and “μ” is the coefficient of viscosity. Typically, SONAR fluid flow meters are operated using an estimated flow viscosity to calculate an estimated Reynolds number for the fluid flow to apply the Reynolds number based calibration. This approach works reasonably well as long as the flow meter is operating at a sufficiently high Reynolds number such that the actual flow measurement is not strongly dependent on the actual Reynolds number. However, for low Reynolds number flows or flows with variable fluid viscosity, errors resulting from differences between the estimated Reynolds number and the actual Reynolds number can lead to significant error in the determined fluid flow rate.
In oil processing applications, the viscosity of oil is often not well known and can change significantly with temperature. Consequently, the Reynolds number of the fluid flow (which is related to the viscosity of the fluid flow) changes significantly as well. The calibration curve shown in FIG. 1 illustrates the relationship between Reynolds number (Re) and the ratio of a measured velocity (Vmeasured; i.e., an uncompensated velocity reported by a flow velocity meter) to an actual velocity (Vactual; i.e., the volumetrically averaged flow velocity) for a given fluid flow as determined by comparing the raw meter output to a calibrated reference flow velocity. The curve illustrated within FIG. 1 can be described mathematically as:
                                          V            measured                                V            actual                          =                  1          +                      c            0                    +                                    c              1                                      Re                              c                2                                                                        (                  Eqn          .                                          ⁢          2                )            Examples of empirically determined values that can be assigned to the variables in Equation 2 include c0=0.03, c1=23.1, and c2=0.61; these values are examples of values that can be used to define the curve in an oil/gas application. Specific values for the variables will depend upon the application at hand. It can be seen from this exemplary calibration curve that if a high Reynolds number approximation (e.g., Re>106) is appropriate for the application at hand, relatively large differences in Reynolds number will yield relatively small changes in the ratio of measured velocity to actual velocity. On the other hand, if a low Reynolds number approximation (e.g., Re<104) is appropriate for the application at hand, relatively small differences in Reynolds number will yield relatively large changes in the ratio of measured velocity to actual velocity. In short, the potential for error in determining a flow parameter (e.g., flow velocity) is greatly increased for a fluid flow meter when sensing low viscosity fluid flows, unless an accurate Reynolds number is used.